A scanning optical system A for use with a printing unit such as a laser printer, copying machine, facsimile machine and the like has generally a configuration as shown in FIG. 10.
In FIG. 10, reference numeral 1 sets forth an LD unit with a semiconductor laser and the like installed therein, which emits a minutely converged beam light 2. Reference numeral 3 sets forth a first optical system which converges the beam light 2 only in a sub-scanning direction (in a direction in which a photosensitive drum rotates). Reference numeral 4 sets forth a polygon mirror which assigns the beam light into a main scanning direction upon rotating. Reference numeral 5 sets forth a second optical system composed of an f.theta. lens, which converges the beam light into the main scanning direction (an axial direction of the photosensitive drum) and the sub-scanning direction to form an electrostatic latent image by the converged imaging on a photosensitive member 6 of the photosensitive drum or the like.
It is to be noted herein that the second optical system 5 is required to have the function of an f.theta. lens compensation (compensation for linearly maintaining a relationship (X=f.theta.) of a rotating angle .theta./2 of the polygon mirror with a scanning position X of the image formation on the photosensitive drum, in addition to the converging action. At this end, in usual occasions, the second optical system comprises a combination of two or three lenses.
On the other hand, in order to reduce a number of parts and to make the scanning optical system compact in size and light in weight, an f.theta. lens composed of a single lens is proposed (Japanese Patent Unexamined Publication No. 5-323,223).
This proposed f.theta. lens is designed so as to have the generating line corresponding to the main scanning direction represented by an aspherical formula as follows: ##EQU2##
where
R is the radius of the curvature; and PA1 K, B.sub.4, B.sub.6, B.sub.8, and B.sub.10 are each an aspherical coefficient; PA1 Cx, K, An, Cy, Bm, Ky, and Gj are each an optional coefficient; and PA1 u, v, and w are each an integer.
and to have the meridional line corresponding to the sub-scanning direction represented by the formula representing a toric plane as follows: ##EQU3##
Further, the technology as disclosed in the above Japanese patent publication is configured such that a slit-shaped diaphragm extending in the main scanning direction is disposed immediately in front of the f.theta. lens so as to make the F-number in the sub-scanning direction constant regardless of the beam spot position on the photosensitive member.
When the f.theta. lens having a single lens configuration composed of the aspherical lens as described above is used, the above patent publication discloses to the effect that the optical performance of the scanning optical system is indicated so as to form a spot having a diameter of 120 .mu.m or larger on the photosensitive member.
In the f.theta. lens using the conventional designing formula as described above, the aspherical formula corresponds to the main scanning direction only. The sub-scanning direction is configured by the toric plane of a simple form and is designed so as to make the F-number constant in the combination with the slit-shaped diaphragm. The conventional configuration, however, suffers from the disadvantage that performance necessary for high resolution cannot be achieved for reasons, for instance, due to the difficulty in making the spot size minute. This may cause the problem particularly when the projection magnification should be made larger so as to extend the scanning width L on the photosensitive member to correspond to, e.g., an A3 paper size.
Therefore, the present invention has the object to provide an f.theta. lens so adapted as to readily make resolution higher by devising an aspherical formula for use in designing, even if it is composed of a single lens and no slit is disposed.